I think the wrong subgroup is chosen for this topic; there is a forum for knot theory.

Moreover, not much is to be learned for a newcomer around the items staked out in your post. The one most important feature is nip, but the nip is difficult to see, and many people that are not even newcomers mistake this fundamental property. The nip is a very elusive feature that is often not where it is thought to be. It can be clearly seen by the list you made up, that you yourself have not unerstood the nip, because your #2 is directly misleading, along with #3.

I think the subject is worth taking up with new students, and all people I know, who teach knotting, do just that.

Thinking a bit more along the same lines, I find an important thing that too often is omitted. It is not an "element" in the knot, but a very important property, and that is the way of tying. Knots in knot books come in two basic categories, and one reason why I like "The Complete Rigger Wire and Rope" by Brion Toss is that he does not omit the tying, the manipulation that must be done to accomplish the knot. There are scores of books showing umpteen knots as what they look like, and sometimes brief directions are given, but mostly just the knot pattern is shown, not the steps you must take to get there. Some knots are rather self-evident in this respect, as the Fisherman's bend or the SquaReef, but other knots may be overly complicated if they are to be tied according to a pattern.

And that topic definitely is more into practical knots than theory.

My argument is that, although it is of some help when you learn, to know what the pattern should look like at a certain stage, it is more important to know how to manipulate the rope to get into that pattern. The Carrick Bend is an excellent example of this, because the best ways of tying do not rely heavily on the shape that can be checked in mid-tying, which is not the shape of the dressed knot, but an intermediate ephemeral state that needs not really be present at any time while tying the knot. The same goes for the "slipknot" way of tying the bowline. The knot pattern, the finished knot, appears from "nowhere" in the final step of pulling it tight; in the transition from one shape to another, the marlingspike hitch rolls over the bowline collar and there it transforms from marlingspike hitch into its final TurNip form (or the more well known bowline nipping turn).

Without those directions, there is little point in learning knots as patterns. Most people applying patterns for tying knots forget them sooner or later if they are not often used knots, which by usage will lead to tying methods that are not so easily forgotten. Then it does not matter a lot whether the method is always the "spilled hitch" or any other way. As long as it is learned as a method, as something done with the hands, it gets into another kind of memory than memorising patterns. The memory for the methods is more basal than the one for patterns. What your hands do will set into subconscious memory in your brain stem, while the memory for patterns is in your conscious memory, an abstract intellectual property, which needs processing before it can take form as a knot. The processing itself may lead to errors. The method that has been delegated down to your hands will not need any thinking to form the knot; it becomes an autonomous process, an act akin to walking or riding a bicycle. The analytical brain is no longer involved, and there is less risk of error.

On challenges such as this I find it valuable to take a couple of ultra simple examples and work them through.

So, starting off - the Simple or Single Hitch exampled in various forms from #1600 onwards. it is a bit of a cheat despite its simplicity because it relies on the presence of an object in order to function, so I will be very interested to see how you approach it.

And second up, the ultra simple Overhand knot as a stopper.

Can you isolate and explain the basic mechanisms at work in these knots? Is there a primary mechanism? Are there 'secondary' mechanisms and if so how are they brought to bear?

snip... Who told you that the simplest thing, near the foundations, are the easiest to explain ? The fifth postulate was unexplained for 2000 years, and the Goldbach s conjecture is still going strong after 250...

Indeed you are right. I found exactly this when I started to develop the Overs Index. But never the less, 'simple' knots are a useful place to start because they are not immediately daunting and at least entice people to 'have a go'. Once an attempt has been made, then because of the clarity of 'simple' knots, any oversights or 'Ah But's' can be identified and considered.

So, going back to the simple hitch you have disassembled into a capstan turn (collar) and a tail nipping 'riding turn' (albeit a very short turn). Great so far - but...

The knot once tied and loaded is not accelerating, so all force vectors must be summed to zero. To do this we must take the forces present in the pole - in other words - the pole is part of the knot...

So to describe the knot, we also have to include the pole within the listed basic functional elements - do you agree?

And if so, then how is this functionality described? An anvil?

On to the Overhand stopper - could we consider it to be two opposing simple hitches to self?

Regarding the practical knot as a machine that converts tensile force into pressure, which builds up and maintains friction that impedes slip, might be a starting point for working on the challenge. I think one of the simplest structures to study in this regard would be the Gleipnir, from which you could continue to the bowline and its eskimo form, as well as the variants of intertangled overhands and the Carrick Bend.

Working along those lines, it might become clearer what features make knots do their work and why they sometimes fail. We might possibly arrive at a definition to what "nip" really is, and maybe where within the knot structure we would prefer to locate it for different purposes.

Still, I think the subject is largely theoretical, although theory and practice should go hand in hand when trying to acquire more knowledge about any subject.

It would be very interesting, and most helpfull, if we could measure the actual friction, induced by those elementary friction mechalisms, on the rope strands that go through/under them. We can further describe those elements, in a more quantified way, if we take into account the specific angle of the relative rotation of the ropes. ( See attached pictures, for some general cases).

Thank you Derek, Those images are representing friction mechanisms, tightened, final parts of knots, as they appear on various places of tightened knots, they are not themselves loose, initial knots ... Image 2 belongs to the classic friction mechanism of the reef family of knots, evidently. Give it another 180 degrees, and you get the friction mechanism of the surgeon knot ( the first of the two). The nipping loop of image 3 belongs to the simple bowline, the Gleipnir, and, if, instead of the two white ropes ( the two legs of the collar of the bowline - the two legs of the Gleipnir) we have a pole, it represents the full riding turn of a hitch. My purpose was to show different angles and notations of the rope turn in a rope embrace-twist or a rope nipping loop. The precise angle of rotation of the plane of the nipping loop, in relation to the rope strands that pass through it, was not meant to be shown in those pictures. ( I tried to keep the pictures as simple/abstract as possible). For example, you should rotate the nipping s loop plane (almost) 90 degrees, and the rope strands axis 180 degrees, to have an image of the Gleipnir nipping loop. Look at a practical knot as a succession, along the rope length, of various rope mechanisms, that reduce the tension forces - and the motion those forces would generate had they were left free to act - from the standing end s 100%, to the tail s 0%. How does this miracle happen ? The tension forces are reduced, dissipated, disappear, through those friction mechanisms, which are the basic elements of almost every practical knot.

A (ingenious) hitch, invented recently by SS369, helped me realize that, in this thread, I had not considered the "oldest" "basic element" known to man, and the most useful one ! It is, essentially, the same friction mechanism that keeps the threads/warp yarns from slipping through a weaved fabric, a human invention well known to every prehistoric housewife that have lived thousands of years ago... In fact, weaved fabrics are nothing else/more than the repetition of this mechanism along and across the area of the cloth. I call it the "ww" element/friction mechanism, ( the weft and warp threads mechanism ), but any suggestion for a more appropriate name would be mush appreciated. It is not made by nipping loops, collars, riding turns or rope embraces/twists, so it can be considered as a fifth "basic element", along with those other four. ( In fact it was, probably, one of the first tangled-rope made tools that were used by man, and, certainly, the first I should have described ! )

The series of the attached pictures show how we arrive, using this ww mechanism, from a 3-warp yarns fabric, to a ww friction hitch. If we double the wefts, so that the one is crossed with the other at each node of the weaved structure, we get a most efficient ww friction hitch, the one devised by SS369. If we follow the path of the white rope/warp, we can see how is is squeezed in its belly, when it passes over the wefts, how it is squeezed in its back, when it passes underneath them, and how it is squeezed in its shoulders, when it passes in between them. This squeezing is the trick of the ww friction mechanism. We can think of many other similar hitches, even a whole class of knots that utilize this same mechanism - or any combination of this mechanism with the other four .

After the publication of the "SS brakehitch" ww friction hitch, I made a little litterature search, and I have discovered that a similar hitch could have been invented by D. Smith, had he replaced the pole of his KC hitch with a rope. (1) Also, the ABoK # 1755b and ABoK#1758 hitches are similar hitches, them too tied on a pole. But it is around a rope that this hitch, and any other similar hitch that is based on this friction mechanism, works at its best, better than any other fiction hitch I know.

Just an example of a ww hitch. (See attached pictures) I count the number of nodes/crossings of the wefts on the "over" and the "under" side of the hitch. In this case, we have a 4o-4u ww hitch. I guess that a 3o-3u ww hitch would be also secure/safe enough, for most materials. The line around which the hitch is tied, the Main line, can be thicker or thinner, and more or less tightened, and these are also factors that determine the minimum required number of nodes/crossing, along the other intrisic characteristics of the rope material, of course. There are many ways, some of them more simple, some more complex, to secure the tail after the last node/crossing with the standing end. I just show one of them here, where the tail exits the knot alongside the standing end. I prefer to weave the two legs of the hitch following a symmetric pattern, (as shown in the pictures), so that they touch the Main line in an orderly and easily inspected way. However, most of the other possible not-so-symmetric weaving patterns would do the job, too.

Those 5 elements are not the basiic elements. When the world was explained by the natural philosophers for the first time, it was a monumental achievement, indeed, to be able ro deduce/reduce the apparent infinity of the number of all things to just 5 essential ones ( water, fire, earth, air, and the fifth element, aether ) - so monumental an achievement that we still remember it, when we speak about something being "quintessential". Then came the atomists, with a single phrase, that the world is made by the natural incarnations of the being and the non-being, the atoms and the void . " If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms ? little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied." Well, the history of science proved that it pays to go from 5 to just 2 !

Let me try a similar reduction in the field of knots... The basic elements that can describe / explain, in a general way, the function of almost every practical knot are 2 : 1. The vertex, the point of contact where two rope segments meet each other - if there is not any, there is not any friction, there is not any practical knot. 2. The angle at which those two rope segments meet each other. Ceteris paribus, the closer the angle to the right angle, the greater the friction between the two rope segments.

The rope embrace(s)/twist(s), the nipping loop(s), the riding turn(s), the collar(s),the wefts and warps, all those 5 friction mechanisms are not but manifestations of the vertex and the angle of contact between two rope segments. So, what does this mean for the knot tyer who just wishes to tie practical knots, and not to think about them ? It means that he should seek knots where the rope segment he wishes to secure ( so it will not slide-slip) is squeezed in place by another one, at as close a right angle to it as possible. Of course, the force with which those two segments are squeezed upon each other is paramount - but this, as well as the other things that determine friction, are covered by this "ceteris paribus"...

Let me close this comment with another relevant quote, by the same person who states the previous one above : " The first principle is that you must not fool yourself, and you are the easiest person to fool."

Do you see anybody else around ? I have also to confess that, sometimes, I speak to Ashley ! I ask him if he would approve a knot that I have tied, and if he would have included it in his bible... so you, for example, would be able to read about it and learn it. Knot tying is a lonely hobby - and it leads to all sorts of hallucinations. Most knot tuyers are talking past each other, as we have seen time and again in this forum. I believe that Ashley himself had wished to warn us about it, with his drawings at Ch. 11, 22 or 27...

( Arguing to one s self ) Elementary, my dear Watson... Two rope segments, being elastic/deformable cylindrical bodies, when they are impressed upon each other by the same force, they bite each other deeper when the area of contact is smaller - i.e., when they meet each other at a right angle. And the 4 convex protuberances/crests/ridges and the 2 concave dents/troughs/grooves that will be generated by this mutual penetration of their bodies, will function as obstacles, and will enhance the friction forces between them way beyond what is expected by the second Amonton s law of friction. On the contrary, when the two segments meet each other at a smaller, oblique, acute angle, those crests and troughs will be less high and deep respectably, so the two segments are more likely to slide on each other on a longer, flattened area, without any tall or deep barriers. Place two tensioned segments of a rope the one above the other in between two parallel planes/plates, and press the one plate upon the other. Then, try to pull the one end of the one segment with some force. The closer the angle A those two segments meet each other to the right angle, the greater the force F required to make the pulled segment slip through would be. The knot, is what you see one a large scale. The rope embrace/twist, the nipping loop, the riding turn, the collar, the weft and the warp, is what you see in a smaller scale. Two inextensible but elastic rods impressed upon each other, so their contact area gets the form of a saddle surface, is what you see in the scale that explains the evidences. And the evidences are that it pays if, in order to secure a free end, you lock it with another one that bites it with a larger force, at a larger angle. Under the same force, the only thing you can do is to make them meet at the right angle - the right angle.